When Harvey Epstein went to sleep on Saturday night, he was a low-profile New York State assemblyman. When he woke up on Sunday morning, he was something of an internet celebrity.

Mr. Epstein was the subject of a “Saturday Night Live” sketch this weekend that spoofed his name — a somewhat unfortunate mash-up of the names of two notorious sexual predators, Harvey Weinstein and Jeffrey Epstein.

The show’s host, the comedian John Mulaney, starred as Harvey Epstein in a campaign ad featuring the candidate struggling to explain to voters that he is neither of the disgraced men. Harvey Epstein is running for the New York City Council in District 2, which includes Greenwich Village, the Lower East Side and parts of southeastern Manhattan.